No. 1024

Title:

Parametric estimation for partially hidden diffusion processes sampled at discrete times

Author(s):

Iacus, Stefano Maria (University of Milan, Italy);
Uchida, Masayuki (Kyushu University);
Yoshida, Nakahiro (University of Tokyo)

Key words:

discrete observations; partially observed systems; diffusion processes

Abstract:

    For a one dimensional diffusion process X= ( X(t) ; $t \in [0,T]$ ), we suppose that X(t) is hidden if it is below some fixed and known threshold $\tau $, but otherwise it is visible. This means a partially hidden diffusion process. The problem treated in this paper is to estimate finite dimensional parameter in both drift and diffusion coefficients under a partially hidden diffusion process obtained by a discrete sampling scheme. It is assumed that the sampling occurs at regularly spaced time intervals of length $h_n$ such that $n h_n=T$. The asymptotic is when $h_n \rightarrow 0$, $T \rightarrow \infty $ and $n h_n^2 \rightarrow 0$ as $n \rightarrow \infty $. Consistency and asymptotic normality for estimators of parameters in both drift and diffusion coefficients are proved.